679. 24 Game

You have 4 cards each containing a number from 1 to 9. You need to judge whether they could operated through*,/,+,-,(,)to get the value of 24.

Example 1:

Input:
 [4, 1, 8, 7]

Output:
 True

Explanation:
 (8-4) * (7-1) = 24

Example 2:

Input:
 [1, 2, 1, 2]

Output:
 False

Note:

1. The division operator / represents real division, not integer division. For example, 4 / (1 - 2/3) = 12.
2. Every operation done is between two numbers. In particular, we cannot use- as a unary operator. For example, with[1, 1, 1, 1]as input, the expression-1 - 1 - 1 - 1is not allowed.
3. You cannot concatenate numbers together. For example, if the input is [1, 2, 1, 2], we cannot write this as 12 + 12.

Discussion

WARNING:

need to take care "0" case, and also since it is double, use eps = 0.001 to double check is better.

dfs(select 2 number, +-*/ + dfs&backtrace(remove 2 number + one posible result).....

class Solution {

    boolean res = false;
    final double eps = 0.001;

    public boolean judgePoint24(int[] nums) {
        List<Double> arr = new ArrayList<>();
        for(int n: nums) arr.add((double) n);
        helper(arr);
        return res;
    }

    private void helper(List<Double> arr){
        if(res) return;
        if(arr.size() == 1){
            if(Math.abs(arr.get(0) - 24.0) < eps)
                res = true;
            return;
        }
        for (int i = 0; i < arr.size(); i++) {
            for (int j = 0; j < i; j++) {
                List<Double> next = new ArrayList<>();
                Double p1 = arr.get(i), p2 = arr.get(j);
                next.addAll(Arrays.asList(p1+p2, p1-p2, p2-p1, p1*p2));
                if(Math.abs(p2) > eps)  next.add(p1/p2);
                if(Math.abs(p1) > eps)  next.add(p2/p1);

                arr.remove(i);
                arr.remove(j);
                for (Double n: next){
                    arr.add(n);
                    helper(arr);
                    arr.remove(arr.size()-1);
                }
                arr.add(j, p2);
                arr.add(i, p1);
            }
        }
    }
}